Another Look at Extraction and Randomization of Groth’s zk-SNARK

Due to the simplicity and performance of zk-SNARKs they are widely used in real-world cryptographic protocols, including blockchain smart contract systems. Simulation Extractability (SE) is a necessary security property for NIZK argument achieve Universal Composability (UC), common requirement such protocols. Most works that investigate SE focus on its strong variant which implies proof non-malleability. In this work we relaxed weaker notion, allows randomization, while guaranteeing statement non-malleability, argue be more natural property. First, show it already achievable by Groth16, arguably most efficient deployed SNARK nowadays. Second, because this, Groth16 can efficiently transformed into black-box weakly NIZK, sufficient UC To support second claim, present compare two practical constructions, both strike different tradeoffs: